Class XII Mathematics

Chapter 5: Continuity and Differentiability

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

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Worksheet Details:

  • Title: Class XII Math: Continuity and Differentiability Printable Sheet
  • Format: Print Optimized CSS stylesheet
  • Sections: Formulas checklist, 5 assessment questions, worked keys

NexPro Education Worksheet

Class XII Mathematics: Continuity and Differentiability

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

Power Rule of Differentiation
\frac{d}{dx}(x^n) = n x^{n-1}
The Chain Rule
\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}

Section II: Answer the Questions

1. Find the rate of change of volume of sphere with respect to its surface area, when radius is 2 cm.

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2. Case-Study 2: A gardener wants to construct a rectangular bed of garden in a circular patch of land. He takes the maximum perimeter of the rectangular region as possible. (Refer to the images given below for calculations) (i) Find the perimeter of rectangle in terms of any one side and radius of circle. (ii) Find critical points to maximize the perimeter of rectangle? (iii) Check for maximum or minimum value of perimeter at critical point. OR (iii) If a rectangle of the maximum perimeter which can be inscribed in a circle of radius 10 cm is square, then the perimeter of region.

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3. An edge of a variable cube is increasing at the rate of 5cm per second. How fast is the volume increasing when the side is 15 cm.

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4. If 2 1,( ) 1, if xxf x if xx ≥{= { <{ , then show that f is not differentiable at x = 1.

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5. The median of an equilateral triangle is increasing at the rate of 2√3 cm/s. Find the rate at which its side is increasing.

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